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Jerk system with broken symmetry; multiple attractors; coexisting bubbles; control of multistability; PSpice simulations

We investigate the impact of a constant force excitation on the dynamics of a simple jerk system with piecewise quadratic nonlinearity.We demonstrate that in the presence of the forcing term, the model is asymmetric yielding more complex and striking bifurcation patterns such as parallel bifurcation branches, coexisting multiple asymmetric attractors, hysteretic dynamics, crises, and coexisting asymmetric bubbles of bifurcation. Accordingly, the coexistence of two, three, four, or five asymmetric periodic and chaotic attractors are reported by changing the model parameters and initial conditions. The control of multistability is investigated by using the method of linear augmentation. We demonstrate that the multistable system can be converted to a monostable state by smoothly adjusting the coupling parameter. A very good agreement is observed between PSpice simulation results and the theoretical study.

LEANDRE KAMDJEU KENGNE^{1 2} JACQUES KENGNE¹ JUSTIN ROGER MBOUPDA PONE¹

1. Laboratories d’Automatique et Informatique Appliquée (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, P.O. Box 134, Bandjoun, Cameroon
2. Laboratory of Electronics and Signal Processing, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon

Published

4 June 2020

Manuscript received

20 October 2019

Manuscript revised

8 February 2020

Accepted

18 February 2020

Early published

Unedited version published online

Final version published online

2 June 2020